Embodiments of the present invention generally relate to statistical approaches for modeling systems and/or processes, and more specifically, the application of statistical models to sensor system processing to extract information from the various outputs produced by a sensor system.
It is often helpful to model physical systems and/or processes in order to gain a better understanding as to how they function. Such models have been shown be very useful for enabling and enhancing a wide variety of practical systems, such as, for example, discrimination systems, prediction systems, recognition and identification systems, etc. Generally, most models can be classified as either deterministic models or statistical models. Deterministic models typical exploit known structures or properties of a system and/or signal, and derive parameters associated therewith. Statistical models can characterize the statistical properties of the system and/or signal. These models can assume the system and/or signal can be characterized by a pre-selected parametric random process, and attempt to estimate parameters associated therewith. Examples of known statistical models include models based upon Gaussian processes, Poison processes, Markov processes, hidden Markov processes, Bayesian theory, etc.
Statistical models which effectively model real-world systems can be sophisticated and therefore can utilize a large number of parameters and/or states. The computations associated with the implementation such models can present a variety of challenges. This is particularly true when the statistical models are used in conjunction with Bayesian theory. For example, probabilities associated with states of a chosen model, and observations of a sensor, will have values ranging between 0 and 1. Complex computations involving these values can produce underflow problems. Underflow problems can occur when numbers reach values which are too small to be accurately represented the finite word lengths used by digital processors. Numbers experiencing underflow errors can be improperly truncated to a value of zero, thus adversely affecting the accuracy of the computation.
Moreover, the relative importance between various parameters associated with the statistical model is often overlooked, thus ignoring information that could improve the efficiency and results of the statistical model. For example, by emphasizing important observations and de-emphasizing those less important, computations can be adapted to improve speed and accuracy, which can be important for real-time, mission-critical systems. Additionally, by emphasizing the relative importance of observations, inaccuracies introduced through assumptions of statistical independence, which are typically made to simplify analysis and/or computations, can be compensated to improve results.